Advertisements
Advertisements
प्रश्न
Evaluate :`intxlogxdx`
Advertisements
उत्तर
`intudv = uv-intvdu`
Choosing u = logx and dv = xdx
`du = 1/xdx `
`v = x^2/2`
`:.intxlogxdx=logx x^2/2-intx^2/2 1/xdx`
`=x^2/2logx-1/2intxdx`
`=x^2/2logx-1/2 x^2/2+C`
`=x^2/2logx-x^2/4+C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
cot x log sin x
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : cos7x
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int x/(x + 2) "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int (logx)^2/x dx` = ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
